Cyber threats continue to escalate in both sophistication and scale, jeopardizing individuals, organizations, and critical infrastructure worldwide. Traditional cybersecurity measures based on static rule sets and signature-based detection often prove inadequate against zero-day exploits, polymorphic malware, and advanced persistent threats. To address these shortcomings, researchers and practitioners are increasingly turning to hybrid cybersecurity frameworks that incorporate machine learning, fuzzy logic, and cryptographic techniques. Machine learning offers dynamic and data-driven threat detection; fuzzy logic accommodates uncertainty and imprecision; while cryptography protects data confidentiality, integrity, and availability. By synergizing these three domains, a multi-faceted security approach emerges—one that can detect novel attacks, adapt to evolving threat landscapes, and secure resources even in distributed resource-constrained environments. This survey explores the theoretical foundations of these hybrid methodologies, reviews cutting-edge applications in phishing detection and IoT security, and discusses advancements in quantum-resistant cryptography. The survey concludes by examining current challenges—including scalability, adversarial robustness, and explainability—and proposing future directions to guide the development of next-generation cybersecurity ecosystems.